summary.nlreg: Summary Method for Nonlinear Heteroscedastic Models
In nlreg: Higher Order Inference for Nonlinear Heteroscedastic Models

Description Usage Arguments Details Value See Also Examples

Returns a summary list for a fitted nonlinear heteroscedastic model.

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## S3 method for class 'nlreg'
summary(object, observed = TRUE, correlation = FALSE, 
        digits = NULL, ...)

`object`	a fitted `nlreg` object. This is assumed to be the result of some fit that produces an object inheriting from the class `nlreg`, in the sense that the components returned by the `nlreg` function will be available.
`observed`	logical argument. If `TRUE`, the observed information is used to calculate the covariance matrix, the expected information otherwise. The default is `TRUE`.
`correlation`	logical argument. If `TRUE`, the correlation matrix for the parameter estimates is computed; default is `TRUE`.
`digits`	the number of significant digits to be printed.
`...`	absorbs any additional argument.

This function is a method for the generic function summary for class nlreg. It can be invoked by calling summary for an object of the appropriate class, or directly by calling summary.nlreg regardless of the class of the object.

A list is returned with the following components:

`coefficients`	a matrix with four columns, containing the MLEs of the regression coefficients, their standard errors, the z-value (or Wald statistic) and the associated p-value based on the standard normal approximation to the distribution of the z statistic.
`varPar`	a matrix with two columns, containing the MLEs of the variance parameters and their standard errors.
`offset`	a numerical vector with a single named element indicating the parameter of interest and the value to which it was fixed while fitting the nonlinear model.
`residuals`	the response residuals from the fit.
`covariance`	the (asymptotic) covariance matrix for the parameter estimates.
`correlation`	the (asymptotic) correlation matrix for the parameter estimates.
`logLik`	the log likelihood from the fit.
`call`	an image of the call that produced the `nlreg` object, but with the arguments all named.
`digits`	then number of significant digits to be printed.
`ws`	the `ws` component of the `nlreg` object.

nlreg.object, summary

data(metsulfuron)
metsulfuron.nl <- 
    nlreg( formula = log(area) ~ log( b1+(b2-b1) / (1+(dose/b4)^b3) ), 
           weights = ~ ( 1+dose^exp(g) )^2, data = metsulfuron, 
           start = c(b1 = 138, b2 = 2470, b3 = 2, b4 = 0.07, g = log(0.3)),
           hoa = TRUE )
##
summary( metsulfuron.nl, digits = 3 )
##
print( summary( metsulfuron.nl )$cov, digits = 3 )
print( summary( metsulfuron.nl, observed = FALSE )$cov, digits = 3 )

Loading required package: statmod
Loading required package: survival

   Package "nlreg" 1.2-2 (2014-03-31) 
    Copyright (C) 2000-2014 R. Bellio & A. R. Brazzale

 This is free software, and you are welcome to redistribute
 it and/or modify it under the terms of the GNU General
 Public License published by the Free Software Foundation.
 Package "nlreg" comes with ABSOLUTELY NO WARRANTY.

 type `help(package="nlreg")' for summary information


differentiating mean and variance function -- may take a while
Call: 
nlreg(formula = log(area) ~ log(b1 + (b2 - b1)/(1 + (dose/b4)^b3)), 
    weights = ~(1 + dose^exp(g))^2, data = metsulfuron, start = c(b1 = 138, 
        b2 = 2470, b3 = 2, b4 = 0.07, g = log(0.3)), hoa = TRUE)

Regression coefficients:
   Estimate Std. Error z value Pr(>|z|)    
b1 1.39e+02   1.68e+01    8.27  < 2e-16 ***
b2 2.47e+03   1.22e+02   20.29  < 2e-16 ***
b3 1.71e+00   2.00e-01    8.53  < 2e-16 ***
b4 7.73e-02   9.78e-03    7.90  2.8e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Variance parameters:
     Estimate Std. Error
g       -1.26      0.484
logs    -3.82      0.226

No interest parameter

Total number of observations: 40
Total number of parameters: 6
-2*Log Likelihood 1.11 

Algorithm converged in 3 iterations
            b1        b2        b3        b4         g      logs
b1   282.50376   -25.828  1.741684 -3.98e-03  1.376745  0.100426
b2   -25.82844 14829.549 -5.287257 -6.53e-01 16.039182  1.038745
b3     1.74168    -5.287  0.040131  1.00e-03  0.008073  0.000646
b4    -0.00398    -0.653  0.001005  9.56e-05 -0.000637 -0.000040
g      1.37674    16.039  0.008073 -6.37e-04  0.234165  0.016970
logs   0.10043     1.039  0.000646 -4.00e-05  0.016970  0.051231
            b1        b2       b3        b4      g   logs
b1    259.4002  -173.237  1.64568  0.010371 0.0000 0.0000
b2   -173.2373 14335.039 -8.05467 -0.712859 0.0000 0.0000
b3      1.6457    -8.055  0.04491  0.001424 0.0000 0.0000
b4      0.0104    -0.713  0.00142  0.000112 0.0000 0.0000
g       0.0000     0.000  0.00000  0.000000 0.2345 0.0171
logs    0.0000     0.000  0.00000  0.000000 0.0171 0.0513